Moments in the duration of play

Eric Bach

Statistics & Probability Letters, 1997, vol. 36, issue 1, 1-7

Abstract: We evaluate moments of the completion time in the classical duration of play problem, equivalent to a symmetric random walk with absorbing endpoints on t-n,h.,n starting from x. We show that the rth cumulant of the absorption time has the form Pr(n2) - Pr(x2) where Pr is a degree r polynomial, and evaluate Pr for r = 1,...,6. Measured in arithmetic operations, our algorithm to compute Pr has amortized cost comparable to the inversion of an r x r matrix. We obtain similar results for unequal initial stakes, and under conditioning on a win by one player. The conditional results settle some open questions due to Beyer.

Keywords: Random; walk; Ruin; problem (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (2)

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